# Inclusion-Exclusion Principle

I'm having a bit of trouble with this, and can't get my numbers to come out correctly.

Here's an example: Get a maximum of n items, composed of the following: x burgers y hot dogs z fruit w napkins

where x,y,z are less than n and w is more than n.

How many different combinations can you make from these?

I would assume it would be (n+4-1) C x - (x+4-1) C x - (y+4-1) C y - (z+4-1) C z + (x+y+4-1) C (x+y) + (x+z+4-1) C (x+z) ...

or am I doing something wrong?

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If $w$ is more than $n$, then how can you have a maximum of $n$ items? –  Cameron Buie Apr 18 at 21:16
The maximum allowable of w is n. Essentially, I could rephrase to w is equal to n. –  BLaZuRE Apr 18 at 21:18
It is hard to get a maximum of $n$ items if we need more than $n$ napkins. Maybe you could state the exact problem that inspired your question. –  André Nicolas Apr 18 at 21:20